The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this note we consider such a problem for the hyperbolic Klein-Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable… (More)
The questions of justification of the Gibbs canonical distribution for systems with elastic impacts are discussed. A special attention is paid to the description of probability measures with densities depending on the system energy.) be conjugate canonical momenta of a Hamiltonian system with n degrees of freedom and a stationary Hamiltonian H(x, y, λ),… (More)
The kinetics of collisionless continuous medium is studied in a bounded region on a curved manifold. We have assumed that in statistical equilibrium, the probability distribution density depends only on the total energy. It is shown that in this case, all the fundamental relations for a multi-dimensional ideal gas in thermal equilibrium hold true. According… (More)
In this article we develop Poincaré ideas about a heat balance of ideal gas considered as a collisionless continuous medium. We obtain the theorems on diffusion in nondegenerate completely integrable systems. As a corollary we show that for any initial distribution the gas will be eventually irreversibly and uniformly distributed over all volume, although… (More)
Traditional derivation of Gibbs canonical distribution and the justification of thermodynamics are based on the assumption concerning an isoenergetic ergodicity of a system of n weakly interacting identical subsystems and passage to the limit n → ∞. In the presented work we develop another approach to these problems assuming that n is fixed and n ≥ 2. The… (More)
In this paper, we present results of simulations of a model of the Galton board for various degrees of elasticity of the ball-to-nail collision.
Human peripheral blood contains RNA in cells and in extracellular membrane vesicles, microvesicles and exosomes, as well as in cell-free ribonucleoproteins. Circulating mRNAs and noncoding RNAs, being internalized, possess the ability to modulate vital processes in recipient cells. In this study, with SOLiD sequencing technology, we performed… (More)
It is suggested that the properties of the mass spectrum of elementary particles could be related with cosmology. Solutions of the Klein-Gordon equation on the Friedmann type manifold with the finite action are constructed. These solutions (actons) have a discrete mass spectrum. We suggest that such solutions could select a universe from cosmological… (More)
Determination of the frequencies and forms of oscillations of non-uniform distributed systems with boundary conditions of the third kind, Appl. Math. Mech.
A collisionless continuous medium in Euclidean space is discussed, i. e. a continuum of free particles moving inertially, without interacting with each other. It is shown that the distribution density of such medium is weakly converging to zero as time increases indefinitely. In the case of Maxwell's velocity distribution of particles, this density… (More)